Autocorrelation functions of a fluid of molecules interacting through steeply repulsive and attractive forces

A new method is presented for an extension of Enskog's approximation for the evaluation of the autocorrelation functions of a fluid, and this approach is used to evaluate these functions when the interaction between the molecules includes both steeply repulsive and steeply attractive forces. Consequently the correlation functions depend upon the temperature in a nontrivial way. As an example, the method is applied to calculate the velocity and force autocorrelation functions of a fluid when the molecules interact through the specific potential, V(r)=4epsilon[(sigma/r)2n-(sigma/r)n] when the parameter n is large. There is a relationship between this model and the "sticky sphere" one which is exploited in the theoretical computations. The results obtained from the theory are compared with molecular dynamics simulation for n=72 and 144 and for a range of temperatures from T=epsilon/kB down to epsilon/3kB. The two approaches agree very well for a range of state points, especially at short times. At later times the theory predicts a more oscillatory behavior than the simulation especially at very low reduced temperatures.